Federal authorities will not end their Y2K anti-terrorist alert until after Jan. 4 — one of the holiest days in the Muslim religion, The Post has learned.

Federal law-enforcement sources said the possibility of a strike on Jan. 4 — the 27th day of the holy month of Ramadan — may be greater than on New Year’s Eve.

Called Lay Lat-al Qadr, the religious holiday translates to “Night of Power” and is considered a time when God determines the course of the world for the following year.

“It’s a very important night for Muslims,” said one source. “And we want to stay on alert until it’s over.”

The fear of terrorist attacks by crazed fundamentalists and other Y2K worries — like computer-generated failures — have forced all city and federal agencies to beef up their forces.

Here’s how they’ll be deployed on New Year’s Eve weekend:

* NYPD — Almost all of its 40,000 officers and most brass will work rotating shifts all weekend. Some 7,000 cops have been assigned to Times Square for New Year’s Eve, almost double the normal number, and extra cops will patrol the subways and major streets.

* PORT AUTHORITY POLICE — All 1,250 officers and brass will work rotating shifts, concentrating on bridges, tunnels and airports. PA spokesman Alan Hicks said that, because of the threat of a car-bomb, there will be zero tolerance of vehicles left parked outside airline terminals.

* FBI — A command post will be set up at 26 Federal Plaza and hundreds of agents will be posted at strategic spots throughout the city.

* CUSTOMS — An extra 150 inspectors along all 301 points of entry along Canadian and Mexican borders. Dozens of extra agents will also be deployed at airports.